Background

This document has nls (non-linear least squares) regression fits using the log-normal functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass growth vs. stand age relationships. This functional form is commonly used in growth analyses, and permits a flexible shape to fit to data with an intermediate maximum (i.e., “hump” shaped) curve. As in our models of biomass growth vs. biomass, we use themass balance biomass growth method for the plot biomass growth (\(G\)) calculation (briefly, plot biomass growth is a function of the change in plot biomass plus any losses due to mortality or harvest over time: \(G_{MB} = (\Delta B + M_t + C_t) / REMPER\), where \(\Delta B\) is change in plot biomass over a census interval ( \(\Delta B = B_{t + \Delta g} - B_t\) ), and \(M_t\) and \(C_t\) is the biomass of trees that died or were harvested, respectively, between two plot measurements. note: \(REMPER\) is time between two plot measurement invetvals (FIA re-measurment period). For additional details see supplementary methods. Models are fitted separately by US ecoprovince.

Hypothetically, the entire functional form of the following non-linear model is considered: \(G = (1 + (yr-1990) \cdot ge/100) \times (1 - \alpha \cdot B_l) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\), where \(G\) is the plot level biomass growth calculated as the sum of tree biomass growth increments, \(B_l\) is the calculated proportion of biomass loss over the census interval, \(StdAge_{t1}\) is the FIA-estimated stand age at the first of two FIA plot tree censuses, \(\Delta PDSI\) is the difference in the growing season (January-August) annual average PDSI values over the FIA plot measurement intervals and a 30-year climate normal (1969-1990), and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(ge\): biomass growth enhancement over time, \(a\): the y-intercept of the curve, \(a +b\): the peak value of \(G\), \(c\): the \(StdAge_{t1}\) value at peak \(G\), and \(d\): the curve shape parameter.

Data have increasing variance in \(G\) with increasing \(StdAge_{t1}\), Thus, weighted nls is the best approach. We explore a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {StdAge_{t1}^2}\) in equal-sample sized plot biomass bins (n=20 where applicable, else n=10) for each ecoprovince. These bins are also used to visualize data means in relation to nls model fit.

Model selection is done to determine the best fitting models, considering the inclusion of \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest), \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or both. \(\Delta PDSI\) is defined the difference in the Palmer drought severity index from January - August for the 10 years preceding the biomass measurement and the 1969-1990 period). We explored \(\Delta PDSI\) using only the summer growing months (June-August) over the same intervals, and analyses were insensitive to that change. Thus, the following three models are considered:

model 1: simple model \(G = (1 + (yr-1990) \cdot ge/100) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\)

model 2: phi model \(G = (1 + (yr-1990) \cdot ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\)

model 3: phi-alpha model \(G = (1 + (yr-1990) \cdot ge/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\)

NOTE:

This document contains all \(G\) observations that meet our plot based filtering criteria:

  1. exclude FIA plots in plantation forests
  2. exclude FIA plots with multiple plot conditions (COND_PROG_UNADJ > 0.95)
  3. exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
  4. exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
  5. exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
  6. exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)

Additionally, in an effort to clean up the data set, we have removed outlier observations, using a quantile threshold approach. We also calculated plot \(G\) using as biomass balance method (see supplementary methods), and the difference between the two methods. Accordingly, we define \(diff_G\) as the difference between tree incremental \(G\) and biomass balance \(G\). We excluded observations which meet the following criteria using a 0.5% quantile (\(QT\)):

  • case A: where the \(QT\) difference in tree incremental \(G\) is > biomass balance plot G (i.e., > 99.5% \(diff_G\) positive outliers)

  • case B: where the \(QT\) difference in tree incremental \(G\) is < mass balance plot G (i.e., < 0.5% \(diff_G\) negative outliers)

  • case C: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., > 99.5% positive outliers)

  • case D: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., < 0.5% negative outliers)

These data set cleaning criteria resulted in the exclusion of 1760 observations.

Below the model fitting procedure is implemented by ecoprovince:

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6869     2901.4                                
## 2   6868     2897.9  1   3.58  8.4899  0.003583 ** 
## 3   6816     2053.4 52 844.44 53.9035 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 29461.42
## 2     2 29454.93
## 3     3 26942.43
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.175722   0.179713   0.978   0.3282    
## phi    0.012249   0.005014   2.443   0.0146 *  
## alpha  0.647140   0.033805  19.143   <2e-16 ***
## a      0.000000   2.567372   0.000   1.0000    
## b      3.468659   2.556471   1.357   0.1749    
## c     31.531484   2.197624  14.348   <2e-16 ***
## d      2.807170   1.242763   2.259   0.0239 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5489 on 6816 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (54 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1  19351     8864.8                                 
## 2  19346     8847.1   5   17.6   7.714 2.946e-07 ***
## 3  18857     4837.7 489 4009.5  31.961 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 83315.42
## 2     2 83265.16
## 3     3 70430.13
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.371292   0.183338   7.480 7.78e-14 ***
## phi    0.022177   0.003247   6.830 8.78e-12 ***
## alpha  0.760152   0.021729  34.984  < 2e-16 ***
## a      0.910942   0.149971   6.074 1.27e-09 ***
## b      1.473072   0.146625  10.047  < 2e-16 ***
## c     21.870646   0.551908  39.627  < 2e-16 ***
## d      1.974895   0.160872  12.276  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5065 on 18857 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3851 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 45 rows containing missing values (geom_point).

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7319     3437.6                                
## 2   7318     3428.8  1   8.85  18.899 1.397e-05 ***
## 3   7254     2939.9 64 488.85  18.846 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 34070.15
## 2     2 34053.26
## 3     3 32723.77
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.731059   0.141839  -5.154 2.62e-07 ***
## phi    0.019550   0.005574   3.507 0.000456 ***
## alpha  0.762600   0.040154  18.992  < 2e-16 ***
## a      2.765891   0.736279   3.757 0.000174 ***
## b      1.866948   0.732518   2.549 0.010834 *  
## c     37.622145   3.355077  11.213  < 2e-16 ***
## d      1.800177   0.531966   3.384 0.000718 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6366 on 7254 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (72 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 6 rows containing missing values (geom_point).

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df  Sum Sq F value  Pr(>F)    
## 1   5044     2430.6                                
## 2   5043     2429.2   1    1.43  2.9759 0.08458 .  
## 3   4823     1030.9 220 1398.27 29.7341 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 25434.95
## 2     2 25433.97
## 3     3 20509.56
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.009831   0.259463  -0.038   0.9698    
## phi    0.021208   0.009599   2.209   0.0272 *  
## alpha  0.754175   0.046147  16.343  < 2e-16 ***
## a      1.873987   0.302299   6.199 6.15e-10 ***
## b      1.512030   0.292885   5.163 2.53e-07 ***
## c     48.261189   3.829558  12.602  < 2e-16 ***
## d      1.759624   0.320971   5.482 4.41e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4623 on 4823 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1015 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 7 rows containing missing values (geom_point).

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Error in nls(fg2_2, data = G_223, start = c(ge = ge.start, a = a.start,  : 
##   parameters without starting value in 'data': phi
##   model      AIC
## 1     1 41571.02
## 2     2       NA
## 3     3 37051.42
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.430060   0.154490  -2.784  0.00539 ** 
## phi    0.000000   0.006842   0.000  1.00000    
## alpha  0.610247   0.043518  14.023  < 2e-16 ***
## a      1.932355   0.632130   3.057  0.00224 ** 
## b      1.921786   0.623188   3.084  0.00205 ** 
## c     27.166651   1.999717  13.585  < 2e-16 ***
## d      1.710858   0.425897   4.017 5.94e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5408 on 8729 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1274 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: does not fit
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 6 rows containing missing values (geom_point).

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df  Sum Sq F value    Pr(>F)    
## 1  13446     7694.3                                  
## 2  13445     7690.4   1    3.88  6.7776  0.009241 ** 
## 3  13194     6475.2 251 1215.26  9.8655 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 70330.21
## 2     2 70325.44
## 3     3 67126.40
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.087217   0.169513   6.414 1.47e-10 ***
## phi    0.007909   0.004533   1.745    0.081 .  
## alpha  0.882295   0.020065  43.973  < 2e-16 ***
## a      2.279044   0.222624  10.237  < 2e-16 ***
## b      3.025758   0.212841  14.216  < 2e-16 ***
## c     17.670790   0.409384  43.164  < 2e-16 ***
## d      1.471406   0.101786  14.456  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7005 on 13194 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (316 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 30 rows containing missing values (geom_point).

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df  Sum Sq F value    Pr(>F)    
## 1  13504     9637.4                                  
## 2  13503     9627.8   1    9.63 13.5009 0.0002394 ***
## 3  13220     8281.9 283 1345.94  7.5918 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 70511.84
## 2     2 70500.33
## 3     3 67414.37
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.090965   0.193247   5.645 1.68e-08 ***
## phi    0.012699   0.004842   2.623  0.00873 ** 
## alpha  0.878838   0.019490  45.091  < 2e-16 ***
## a      3.024828   0.116153  26.042  < 2e-16 ***
## b      2.215523   0.109583  20.218  < 2e-16 ***
## c     15.764213   0.430152  36.648  < 2e-16 ***
## d      0.898401   0.050710  17.716  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7915 on 13220 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (402 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 66 rows containing missing values (geom_point).

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Error in nls(fg2_1, data = G_234, start = c(ge = ge.start, a = a.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
## Error in nls(fg2_2, data = G_234, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
##   model      AIC
## 1     1       NA
## 2     2       NA
## 3     3 6972.096
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     1.49422    1.17974   1.267 0.205534    
## phi    0.00000    0.02294   0.000 1.000000    
## alpha  0.81742    0.08559   9.550  < 2e-16 ***
## a      3.25252    0.62763   5.182 2.54e-07 ***
## b      1.60883    0.52220   3.081 0.002107 ** 
## c     17.83216    2.52293   7.068 2.54e-12 ***
## d      0.68248    0.20369   3.351 0.000829 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8154 on 1315 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (66 observations deleted due to missingness)

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: fits ## plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90233, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.3394, p-value = 9.324e-08
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 5 rows containing missing values (geom_point).

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value Pr(>F)    
## 1   1888     981.71                              
## 2   1887     981.71   1   0.00   0.000      1    
## 3   1772     366.23 115 615.48  25.895 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 9553.901
## 2     2 9555.901
## 3     3 7360.235
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     0.42081    0.50776   0.829 0.407354    
## phi    0.01688    0.01280   1.319 0.187293    
## alpha  0.39359    0.10471   3.759 0.000176 ***
## a      0.00000    7.48138   0.000 1.000000    
## b      2.75477    7.47785   0.368 0.712626    
## c     29.12100    7.86923   3.701 0.000222 ***
## d      3.98974    6.44419   0.619 0.535915    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4546 on 1772 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (516 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.82033, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.3049, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 2 rows containing missing values (geom_point).

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1    710    1009.74                                 
## 2    709     993.90  1  15.841 11.3005 0.0008165 ***
## 3    666     874.66 43 119.237  2.1114 6.801e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3560.631
## 2     2 3551.325
## 3     3 3316.266
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     1.47159    1.57754   0.933 0.351240    
## phi    0.07749    0.03138   2.470 0.013771 *  
## alpha  0.57688    0.18640   3.095 0.002052 ** 
## a      0.79526    0.55225   1.440 0.150329    
## b      2.20051    0.75723   2.906 0.003782 ** 
## c     15.62073    1.93811   8.060 3.54e-15 ***
## d      1.28673    0.37411   3.439 0.000619 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.146 on 666 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (44 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92581, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.18, p-value = 2.915e-05
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 2 rows containing missing values (geom_point).

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

322 - American Semidesert and Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

331 - Great Plains/Palouse Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

332 - Great Plains Steppe

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

341 - Intermountain Semi-desert & Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

342 - Intermountain Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   6765     1889.9                                 
## 2   6764     1879.6  1  10.281  36.998 1.247e-09 ***
## 3   6740     1749.8 24 129.814  20.835 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 25839.54
## 2     2 25804.61
## 3     3 25259.82
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.850679   0.215547   3.947 8.01e-05 ***
## phi    0.023449   0.004584   5.116 3.21e-07 ***
## alpha  0.627001   0.029034  21.595  < 2e-16 ***
## a      2.395907   0.162710  14.725  < 2e-16 ***
## b      0.669053   0.118100   5.665 1.53e-08 ***
## c     29.566789   2.152052  13.739  < 2e-16 ***
## d      1.014318   0.225290   4.502 6.84e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5095 on 6740 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (25 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   8308     4863.8                             
## 2   8307     4863.8  1   0.00   0.000 0.9998    
## 3   8252     4464.8 55 398.96  13.407 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 40946.90
## 2     2 40948.90
## 3     3 40032.35
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.379874   0.205871   1.845    0.065 .  
## phi    0.000000   0.006671   0.000    1.000    
## alpha  0.831928   0.056198  14.803  < 2e-16 ***
## a      2.837387   0.308199   9.206  < 2e-16 ***
## b      1.567034   0.260530   6.015 1.88e-09 ***
## c     26.790439   2.070126  12.941  < 2e-16 ***
## d      1.190169   0.241636   4.925 8.58e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7356 on 8252 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (56 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 2 rows containing missing values (geom_point).

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    890     537.81                                
## 2    889     537.81  1  0.000  0.0000         1    
## 3    882     515.61  7 22.204  5.4262 4.128e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3747.851
## 2     2 3749.851
## 3     3 3696.417
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     3.88192    2.09581   1.852 0.064327 .  
## phi    0.00000    0.02552   0.000 1.000000    
## alpha  0.89195    0.14974   5.957 3.72e-09 ***
## a      1.39795    0.34310   4.074 5.03e-05 ***
## b      0.87413    0.32246   2.711 0.006842 ** 
## c     32.18412    2.98916  10.767  < 2e-16 ***
## d      0.39970    0.11321   3.530 0.000436 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7646 on 882 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (7 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9565, p-value = 1.42e-15
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.926, p-value = 0.05411
## alternative hypothesis: two.sided

predict and plot

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1000     560.60                                
## 2    999     552.70  1  7.902 14.2827 0.0001666 ***
## 3    986     491.02 13 61.681  9.5278 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4301.062
## 2     2 4288.796
## 3     3 4128.190
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     2.83325    1.71080   1.656  0.09802 .  
## phi    0.06188    0.02469   2.506  0.01235 *  
## alpha  0.83322    0.10345   8.055 2.29e-15 ***
## a      1.56723    0.38924   4.026 6.10e-05 ***
## b      1.02877    0.36360   2.829  0.00476 ** 
## c      8.22702    4.42140   1.861  0.06308 .  
## d      1.36317    0.64509   2.113  0.03484 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7057 on 986 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (13 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96553, p-value = 1.401e-14
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.6924, p-value = 2.196e-11
## alternative hypothesis: two.sided

predict and plot

plotting 2

M242 - Cascade Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)    
## 1   3140     2646.7                              
## 2   3139     2646.6  1   0.127  0.1508 0.6978    
## 3   3126     2505.4 13 141.214 13.5534 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 17325.39
## 2     2 17327.24
## 3     3 17111.31
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -1.68631    0.28189  -5.982 2.45e-09 ***
## phi    0.03281    0.01781   1.842   0.0656 .  
## alpha  1.00975    0.07255  13.918  < 2e-16 ***
## a      6.71584    0.63106  10.642  < 2e-16 ***
## b      5.11669    0.94827   5.396 7.33e-08 ***
## c     33.89591    1.57146  21.570  < 2e-16 ***
## d      0.34932    0.05348   6.531 7.58e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8952 on 3126 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (91 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92849, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -13.637, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 14 rows containing missing values (geom_point).

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq  F value    Pr(>F)    
## 1   1681     601.84                                 
## 2   1680     564.32  1 37.518 111.6926 < 2.2e-16 ***
## 3   1667     553.48 13 10.846   2.5128  0.002055 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 8778.075
## 2     2 8671.552
## 3     3 8594.167
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -2.11595    0.28437  -7.441 1.59e-13 ***
## phi    0.22245    0.01615  13.775  < 2e-16 ***
## alpha  0.63860    0.11361   5.621 2.22e-08 ***
## a      0.00000   15.61528   0.000    1.000    
## b      9.69748   15.55236   0.624    0.533    
## c     41.76697    9.84387   4.243 2.33e-05 ***
## d      3.08338    3.19925   0.964    0.335    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5762 on 1667 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (303 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89623, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.89111, p-value = 0.3729
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 9 rows containing missing values (geom_point).

plotting 2

M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    360     174.32                              
## 2    359     171.92  1 2.4066  5.0256 0.025586 * 
## 3    358     167.42  1 4.4942  9.6100 0.002088 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 1014.707
## 2     2 1011.633
## 3     3 1003.964
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -2.35177    0.35314  -6.660 1.04e-10 ***
## phi    0.04249    0.03040   1.398 0.163042    
## alpha  0.53619    0.15685   3.418 0.000702 ***
## a      0.00000    5.08614   0.000 1.000000    
## b      3.54153    5.16095   0.686 0.493020    
## c     60.11727   17.06244   3.523 0.000481 ***
## d      2.03511    2.15536   0.944 0.345698    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6839 on 358 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94875, p-value = 6.111e-10
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.2763, p-value = 0.2018
## alternative hypothesis: two.sided

predict and plot

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   1736     1579.8                                 
## 2   1735     1566.4  1  13.436  14.882 0.0001186 ***
## 3   1718     1408.5 17 157.914  11.330 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 5243.073
## 2     2 5230.203
## 3     3 5027.467
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.43950    0.72527  -0.606 0.544611    
## phi    0.07592    0.01579   4.808 1.66e-06 ***
## alpha  0.60685    0.06216   9.762  < 2e-16 ***
## a      0.50536    0.45171   1.119 0.263388    
## b      1.39227    0.48322   2.881 0.004010 ** 
## c     52.27252    4.00432  13.054  < 2e-16 ***
## d      1.68705    0.44665   3.777 0.000164 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9055 on 1718 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (31 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.85663, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.9566, p-value = 7.173e-07
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 7 rows containing missing values (geom_point).

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)    
## 1   2527     1847.2                               
## 2   2526     1843.7  1   3.498  4.7926 0.02867 *  
## 3   2484     1677.5 42 166.126  5.8569 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 9333.635
## 2     2 9330.836
## 3     3 9043.459
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.70989    0.51904  -1.368 0.171534    
## phi    0.02565    0.01852   1.385 0.166144    
## alpha  0.82947    0.05540  14.972  < 2e-16 ***
## a      0.77371    0.65074   1.189 0.234570    
## b      1.89238    0.68717   2.754 0.005932 ** 
## c     61.36711    5.77057  10.635  < 2e-16 ***
## d      2.10362    0.57479   3.660 0.000258 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8218 on 2484 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (121 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.88452, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.8136, p-value = 9.522e-12
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 28 rows containing missing values (geom_point).

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   1699     872.98                             
## 2   1698     871.99  1  0.987  1.9228 0.1657    
## 3   1669     777.32 29 94.663  7.0087 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6978.661
## 2     2 6978.732
## 3     3 6737.088
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     0.07404    0.85812   0.086    0.931    
## phi    0.00470    0.02034   0.231    0.817    
## alpha  0.85634    0.05823  14.706  < 2e-16 ***
## a      1.43729    0.29460   4.879 1.17e-06 ***
## b      2.34177    0.46362   5.051 4.88e-07 ***
## c     49.87354    2.07374  24.050  < 2e-16 ***
## d      1.09119    0.09957  10.959  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6825 on 1669 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (77 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93034, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.5801, p-value = 2.403e-08
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 14 rows containing missing values (geom_point).

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Error in nls(fg2_1, data = G_M334, start = c(ge = ge.start, a = a.start,  : 
##   Convergence failure: singular convergence (7)
## Error in nls(fg2_2, data = G_M334, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
##   model      AIC
## 1     1       NA
## 2     2       NA
## 3     3 1377.238
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      -3.74019    0.09721 -38.477  < 2e-16 ***
## phi      0.09723    0.02834   3.431 0.000674 ***
## alpha    0.75357    0.18506   4.072 5.77e-05 ***
## a        0.00000 1728.64931   0.000 1.000000    
## b        5.19647 1728.30661   0.003 0.997603    
## c       67.00547  108.86401   0.615 0.538629    
## d        4.59576  789.29208   0.006 0.995358    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4652 on 348 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (104 observations deleted due to missingness)

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91388, p-value = 2.264e-13
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.4979, p-value = 0.01249
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1 rows containing missing values (geom_point).

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod
211 Northeastern Mixed Forest 3
212 Laurentian Mixed Forest 3
221 Eastern Broadleaf Forest 3
222 Midwest Broadleaf Forest 3
223 Central Interior Broadleaf Forest 3
231 Southeastern Mixed Forest 3
232 Outer Coastal Plain Mixed Forest 3
234 Lower Mississippi Riverine Forest 3
242 Pacific Lowland Mixed Forest NA
251 Prairie Parkland (Temperate) 3
255 Prairie Parkland (Subtropical) 3
261 California Coastal Chaparral Forest and Shrub NA
262 California Dry Steppe NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest NA
313 Colorado Plateau Semi-Desert NA
315 Southwest Plateau and Plains Dry Steppe and Shrub NA
321 Chihuahuan Semi-Desert NA
322 American Semidesert and Desert NA
331 Great Plains/Palouse Dry Steppe NA
332 Great Plains Steppe NA
341 Intermountain Semi-Desert and Desert NA
342 Intermountain Semi-Desert NA
411 Everglades NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 3
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 3
M223 Ozark Broadleaf Forest Meadow 3
M231 Ouachita Mixed Forest 3
M242 Cascade Mixed Forest 3
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 3
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow 3
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow 3
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 3
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 3
M334 Black Hills Coniferous Forest 3
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow NA

table by ecoprovince

Code Ecoregion region n.obs n.plots ge ge.variance ge.2.5 ge.97.5 phi phi.variance phi.2.5 phi.97.5 alpha alpha.variance alpha.2.5 alpha.97.5 a a.2.5 a.97.5 b b.2.5 b.97.5 c c.2.5 c.97.5 d d.2.5 d.97.5
211 Northeastern Mixed Forest east 6877 2876 0.1757217 0.0322968 -0.1765723 0.5280157 0.0122492 0.0000251 0.0024208 0.0220776 0.6471401 0.0011428 0.5808719 0.7134083 0.0000000 -5.0328500 5.032850 3.4686588 -1.5428214 8.4801390 31.531484 27.2234549 35.83951 2.8071701 0.3709672 5.2433731
212 Laurentian Mixed Forest east 22715 9499 1.3712921 0.0336129 1.0119325 1.7306517 0.0221771 0.0000105 0.0158122 0.0285419 0.7601525 0.0004721 0.7175621 0.8027429 0.9109417 0.6169850 1.204898 1.4730721 1.1856744 1.7604698 21.870646 20.7888568 22.95243 1.9748949 1.6595713 2.2902184
221 Eastern Broadleaf Forest east 7333 3571 -0.7310590 0.0201183 -1.0091047 -0.4530133 0.0195496 0.0000311 0.0086221 0.0304770 0.7625996 0.0016124 0.6838854 0.8413138 2.7658911 1.3225695 4.209213 1.8669476 0.4309986 3.3028965 37.622145 31.0452181 44.19907 1.8001769 0.7573684 2.8429855
222 Midwest Broadleaf Forest east 5845 2589 -0.0098311 0.0673213 -0.5184979 0.4988356 0.0212082 0.0000921 0.0023900 0.0400265 0.7541747 0.0021295 0.6637062 0.8446432 1.8739873 1.2813427 2.466632 1.5120302 0.9378419 2.0862185 48.261189 40.7535103 55.76887 1.7596238 1.1303752 2.3888723
223 Central Interior Broadleaf Forest east 10010 3864 -0.4300605 0.0238672 -0.7328976 -0.1272234 0.0000000 0.0000468 -0.0134128 0.0134128 0.6102470 0.0018938 0.5249408 0.6955533 1.9323553 0.6932307 3.171480 1.9217860 0.7001901 3.1433819 27.166651 23.2467347 31.08657 1.7108584 0.8760004 2.5457164
231 Southeastern Mixed Forest east 13517 6193 1.0872168 0.0287345 0.7549477 1.4194859 0.0079088 0.0000205 -0.0009756 0.0167932 0.8822954 0.0004026 0.8429659 0.9216249 2.2790445 1.8426686 2.715420 3.0257576 2.6085578 3.4429573 17.670790 16.8683377 18.47324 1.4714062 1.2718904 1.6709221
232 Outer Coastal Plain Mixed Forest east 13629 6626 1.0909652 0.0373445 0.7121729 1.4697576 0.0126993 0.0000234 0.0032082 0.0221903 0.8788383 0.0003799 0.8406343 0.9170423 3.0248278 2.7971517 3.252504 2.2155226 2.0007250 2.4303203 15.764214 14.9210544 16.60737 0.8984005 0.7990007 0.9978004
234 Lower Mississippi Riverine Forest east 1388 778 1.4942188 1.3917795 -0.8201536 3.8085911 0.0000000 0.0005261 -0.0449981 0.0449981 0.8174169 0.0073257 0.6495081 0.9853257 3.2525184 2.0212509 4.483786 1.6088252 0.5843812 2.6332693 17.832162 12.8827518 22.78157 0.6824795 0.2828883 1.0820707
242 Pacific Lowland Mixed Forest pacific 83 83 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
251 Prairie Parkland (Temperate) east 2295 906 0.4208094 0.2578200 -0.5750617 1.4166806 0.0168846 0.0001638 -0.0082195 0.0419888 0.3935897 0.0109646 0.1882173 0.5989622 0.0000000 -14.6732552 14.673255 2.7547694 -11.9115628 17.4211017 29.121003 13.6870608 44.55495 3.9897412 -8.6492645 16.6287469
255 Prairie Parkland (Subtropical) east 717 319 1.4715937 2.4886282 -1.6259544 4.5691419 0.0774910 0.0009845 0.0158825 0.1390995 0.5768757 0.0347441 0.2108777 0.9428737 0.7952626 -0.2891058 1.879631 2.2005057 0.7136645 3.6873469 15.620730 11.8151965 19.42626 1.2867271 0.5521553 2.0212988
261 California Coastal Chaparral Forest and Shrub pacific 25 25 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 163 161 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert interior west 218 218 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 4 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 9 9 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 3 3 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 331 255 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe interior west 232 128 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
341 Intermountain Semi-Desert and Desert interior west 66 64 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert interior west 124 123 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
411 Everglades east 96 63 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 6772 3006 0.8506786 0.0464607 0.4281377 1.2732195 0.0234487 0.0000210 0.0144631 0.0324344 0.6270009 0.0008430 0.5700847 0.6839171 2.3959066 2.0769427 2.714870 0.6690529 0.4375387 0.9005672 29.566789 25.3480873 33.78549 1.0143181 0.5726788 1.4559574
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 8315 3810 0.3798736 0.0423827 -0.0236846 0.7834318 0.0000000 0.0000445 -0.0130773 0.0130773 0.8319284 0.0031582 0.7217658 0.9420911 2.8373869 2.2332400 3.441534 1.5670341 1.0563296 2.0777385 26.790439 22.7324710 30.84841 1.1901695 0.7165016 1.6638373
M223 Ozark Broadleaf Forest Meadow east 896 349 3.8819194 4.3924187 -0.2314369 7.9952758 0.0000000 0.0006513 -0.0500874 0.0500874 0.8919472 0.0224223 0.5980573 1.1858370 1.3979515 0.7245642 2.071339 0.8741318 0.2412521 1.5070115 32.184124 26.3174182 38.05083 0.3996992 0.1774979 0.6219005
M231 Ouachita Mixed Forest east 1006 495 2.8332512 2.9268445 -0.5239808 6.1904831 0.0618791 0.0006095 0.0134331 0.1103252 0.8332165 0.0107009 0.6302183 1.0362147 1.5672319 0.8033972 2.331067 1.0287701 0.3152511 1.7422890 8.227022 -0.4494142 16.90346 1.3631726 0.0972655 2.6290796
M242 Cascade Mixed Forest pacific 3224 3207 -1.6863076 0.0794597 -2.2390078 -1.1336075 0.0328095 0.0003173 -0.0021192 0.0677381 1.0097463 0.0052638 0.8674925 1.1520002 6.7158353 5.4784970 7.953174 5.1166890 3.2573890 6.9759891 33.895910 30.8147167 36.97710 0.3493224 0.2444564 0.4541883
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 1977 1807 -2.1159462 0.0808660 -2.6737052 -1.5581872 0.2224490 0.0002608 0.1907744 0.2541236 0.6386041 0.0129071 0.4157720 0.8614363 0.0000000 -30.6276147 30.627615 9.6974846 -20.8067314 40.2017006 41.766965 22.4593149 61.07462 3.0833786 -3.1915868 9.3583439
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 30 26 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 367 367 -2.3517700 0.1247053 -3.0462524 -1.6572876 0.0424936 0.0009242 -0.0172926 0.1022799 0.5361936 0.0246028 0.2277251 0.8446621 0.0000000 -10.0024735 10.002474 3.5415332 -6.6080480 13.6911145 60.117269 26.5620659 93.67247 2.0351118 -2.2036387 6.2738624
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 1756 1756 -0.4394975 0.5260216 -1.8620095 0.9830145 0.0759209 0.0002494 0.0449473 0.1068945 0.6068543 0.0038642 0.4849311 0.7287774 0.5053632 -0.3805895 1.391316 1.3922719 0.4445098 2.3400341 52.272520 44.4186644 60.12638 1.6870535 0.8110138 2.5630932
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 2612 2602 -0.7098862 0.2694041 -1.7276847 0.3079123 0.0256535 0.0003430 -0.0106646 0.0619715 0.8294692 0.0030694 0.7208304 0.9381079 0.7737062 -0.5023491 2.049762 1.8923794 0.5448956 3.2398632 61.367106 50.0514907 72.68272 2.1036231 0.9765099 3.2307362
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 1753 1742 0.0740389 0.7363628 -1.6090579 1.7571357 0.0047003 0.0004137 -0.0351939 0.0445945 0.8563386 0.0033909 0.7421249 0.9705523 1.4372869 0.8594631 2.015111 2.3417687 1.4324324 3.2511050 49.873539 45.8061307 53.94095 1.0911851 0.8958840 1.2864863
M334 Black Hills Coniferous Forest interior west 459 181 -3.7401899 0.0094489 -3.9313741 -3.5490057 0.0972250 0.0008030 0.0414904 0.1529597 0.7535661 0.0342465 0.3895930 1.1175392 0.0000000 -3399.9147613 3399.914761 5.1964723 -3394.0442740 3404.4372185 67.005467 -147.1087216 281.11966 4.5957627 -1547.7872271 1556.9787525
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 220 220 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I
## Warning: package 'ggnewscale' was built under R version 4.2.1
## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

plot phi (effect of DeltaPDSI)

plot alpha (biomass growth compensation effect)

plot a coefficient

## Warning: Removed 15 rows containing missing values (geom_point).

plot b coefficient

## Warning: Removed 15 rows containing missing values (geom_point).

plot c coefficient

## Warning: Removed 1 rows containing missing values (geom_hline).
## Warning: Removed 16 rows containing missing values (geom_point).

plot d coefficient

## Warning: Removed 15 rows containing missing values (geom_point).

Caclulations - weighted averages

ge (stand biomass growth enhancement factor in % 2000-2021)

##          region weighted.ge weighted.ge.std_Error 95 % CI, upper 95 % CI, lower
## 1     entire US  0.32298228            0.07217642      0.4644481      0.1815165
## 2       pacific -0.15936993            0.01795158     -0.1241848     -0.1945550
## 3          east  0.55192458            0.05647196      0.6626096      0.4412395
## 4 interior west -0.06957237            0.04120795      0.0111952     -0.1503399

phi (effect of DeltaPDSI)

##          region weighted.phi weighted.phi.std_Error 95 % CI, upper
## 1     entire US  0.024056979            0.002108731    0.028190093
## 2       pacific  0.008755896            0.001107489    0.010926574
## 3          east  0.011132791            0.001371046    0.013820041
## 4 interior west  0.004168293            0.001157778    0.006437538
##   95 % CI, lower
## 1    0.019923866
## 2    0.006585218
## 3    0.008445541
## 4    0.001899048

alpha (biomass growth compensation effect)

##          region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1     entire US     0.75612701              0.010455205     0.77661921
## 2       pacific     0.07582588              0.005356807     0.08632522
## 3          east     0.59313953              0.008153682     0.60912075
## 4 interior west     0.08716159              0.003759442     0.09453010
##   95 % CI, lower
## 1     0.73563480
## 2     0.06532654
## 3     0.57715832
## 4     0.07979309